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A079474 Triangular array: for s=0 to r-1, a(r,s) = p(s)^(r-s), where p(s) is the s-th primorial number. (p(0)=1, p(1)=2, p(2)=2*3, p(3)=2*3*5,...).

%I A079474 #23 Dec 07 2019 08:14:26
%S A079474 1,1,2,1,4,6,1,8,36,30,1,16,216,900,210,1,32,1296,27000,44100,2310,1,
%T A079474 64,7776,810000,9261000,5336100,30030,1,128,46656,24300000,1944810000,
%U A079474 12326391000,901800900,510510,1,256,279936,729000000,408410100000
%N A079474 Triangular array: for s=0 to r-1, a(r,s) = p(s)^(r-s), where p(s) is the s-th primorial number. (p(0)=1, p(1)=2, p(2)=2*3, p(3)=2*3*5,...).
%C A079474 In the expansion of [1+x+x^2+...+x^(r-s)]^s, the x^n coefficient states how many factors of a(r,s) have n prime factors.
%C A079474 As a square array A(n,k) n>=0 k>=1 read by descending antidiagonals, A(n,k) when n>=1 is the least common period over the positive integers of the occurrence of the first n prime numbers as the k-th least operand in the respective integers' prime factorizations (written without exponents). - _Peter Munn_, Jan 25 2017
%e A079474 Triangle starts
%e A079474   1;
%e A079474   1,  2;
%e A079474   1,  4,    6;
%e A079474   1,  8,   36,    30;
%e A079474   1, 16,  216,   900,   210;
%e A079474   1, 32, 1296, 27000, 44100, 2310;
%e A079474   ...
%p A079474 p:= proc(n) option remember; `if`(n=0, 1, ithprime(n)*p(n-1)) end:
%p A079474 a:= (r, s)-> p(s)^(r-s):
%p A079474 seq(seq(a(r, s), s=0..r-1), r=0..10);  # _Alois P. Heinz_, Aug 22 2019
%t A079474 p[0] = 1; p[s_] := p[s] = Prime[s] p[s-1];
%t A079474 a[r_, s_] := p[s]^(r-s);
%t A079474 Table[a[r, s], {r, 0, 10}, {s, 0, r-1}] // Flatten (* _Jean-François Alcover_, Dec 07 2019 *)
%Y A079474 Cf. A002110, A007318, A008287, A027907, A036035, A061742, A074139.
%Y A079474 a(2n,n) gives A181555.
%K A079474 nonn,tabl
%O A079474 1,3
%A A079474 _Alford Arnold_, Jan 15 2003
%E A079474 Edited by _Don Reble_, Nov 02 2005